

A355055


Number of achiral multidimensional nominoes with cell centers determining n3 space.


5



1, 5, 23, 115, 668, 3401, 16469, 74410, 317612, 1287147, 5015932, 18920467, 69496943, 249618639, 879998839, 3053446651, 10452089459, 35360685297, 118416973230, 393038044024, 1294335897888, 4232938101229, 13757913332396
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OFFSET

4,2


COMMENTS

Multidimensional polyominoes are connected sets of cells of regular tilings with SchlĂ¤fli symbols {oo}, {4,4}, {4,3,4}, {4,3,3,4}, etc. Each tile is a regular orthotope (hypercube). This sequence is obtained using the first formula below. An achiral polyomino is identical to its reflection.


LINKS

Table of n, a(n) for n=4..26.
W. F. Lunnon, Counting multidimensional polyominoes. Computer Journal 18 (1975), no. 4, pp. 366367.


FORMULA

a(n) = A355053(n)  A355054(n) = 2*A355053(n)  A355052(n) = A355052(n)  2*A355054(n).
a(n) = 2*A049430(n,n3)  A195738(n,n3), Lunnon's DE and DR arrays.


EXAMPLE

a(4)=1 as there is only one tetromino in onespace. a(5)=5 because there are 5 achiral pentominoes in 2space, excluding the 1D straight pentomino.


CROSSREFS

Cf. A355052 (oriented), A355053 (unoriented), A355054 (chiral), A355056 (asymmetric), A191092 (fixed), A355050 (orthoplex), A195738 (Lunnon's DR), A049430 (Lunnon's DE).
Sequence in context: A299589 A113284 A104090 * A073596 A167248 A321798
Adjacent sequences: A355052 A355053 A355054 * A355056 A355057 A355058


KEYWORD

nonn,easy


AUTHOR

Robert A. Russell, Jun 16 2022


STATUS

approved



